Electrical Mobility

Storyboard

>Model

ID:(1527, 0)



Stokes force

Equation

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The resistance is defined in terms of the fluid viscosity and the sphere's velocity as follows:

$ F_v = b v $



Stokes explicitly calculated the resistance experienced by the sphere and determined that viscosity is proportional to the sphere's radius and its velocity, leading to the following equation for resistance:

$ F_v =6 \pi \eta r v $

$\pi$
Pi
3.1415927
$rad$
5057
$r$
Radius of a sphere
$m$
10331
$v$
Speed
$m/s$
6029
$F_v$
Viscose force
$N$
4979
$\eta$
Viscosity
$Pa s$
5422

ID:(4871, 0)



Particle velocity in electric field

Equation

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A charged particle q in an electric field \ vec {E} means that a force equal to

$ F = q E $



This force is opposed by a force due to the effect of the medium that can be modeled by Stokes law

$ F_v =6 \pi \eta r v $



If both forces are equalized, it is obtained that the particle moves with a constant speed equal to

$ \vec{v} = \mu \vec{E} $



with mobility equal to

$ \mu =\displaystyle\frac{ q }{6 \pi \eta a }$

ID:(11997, 0)



Particle mobility in electric field

Equation

>Top, >Model


To equalize the force caused by the electric field

$ F = q E $



with the opposing force that is modeled with Stokes law

$ F_v =6 \pi \eta r v $



the relationship is obtained

$ \vec{v} = \mu \vec{E} $



with mobility equal to

$ \mu =\displaystyle\frac{ q }{6 \pi \eta a }$

ID:(11998, 0)